Skip to content

unique_perms

Unique permutations is used to calculate the unique permutations of a list/vector and their count.

UniqueElement dataclass 

UniqueElement(value: int, occurrences: int)

Class for unique elements to keep track of occurrences.

unique_perms 

unique_perms(
    elements: list[int],
) -> Generator[tuple[int, ...], None, None]

Determine the number of unique permutations of a list.

Parameters:

  • elements (list[int]) –

    List of integers.

Returns:

  • None –

    The number of possible permutations possible.

Examples:

Consider the following vector

\[ \left[1, 1, 2, 2, 1, 2, 1, 3, 3, 3\right]. \]

The number of possible permutations possible with the above vector is \(4200\). This can be obtained using the |toqito⟩ package as follows.

from toqito.perms import unique_perms

vec_nums = [1, 1, 2, 2, 1, 2, 1, 3, 3, 3]

print(len(list(unique_perms(vec_nums))))

4200
Source code in toqito/perms/unique_perms.py 
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
def unique_perms(elements: list[int]) -> Generator[tuple[int, ...], None, None]:
    r"""Determine the number of unique permutations of a list.

    Args:
        elements: List of integers.

    Returns:
        The number of possible permutations possible.

    Examples:
        Consider the following vector

        \[
            \left[1, 1, 2, 2, 1, 2, 1, 3, 3, 3\right].
        \]

        The number of possible permutations possible with the above vector is \(4200\). This can be
        obtained using the `|toqito⟩` package as follows.

        ```python exec="1" source="above" result="text"
        from toqito.perms import unique_perms

        vec_nums = [1, 1, 2, 2, 1, 2, 1, 3, 3, 3]

        print(len(list(unique_perms(vec_nums))))
        ```

    """
    elem_set = set(elements)
    list_unique = [UniqueElement(value=i, occurrences=elements.count(i)) for i in elem_set]
    len_elems = len(elements)

    return perm_unique_helper(list_unique, [0] * len_elems, len_elems - 1)

perm_unique_helper 

perm_unique_helper(
    list_unique: list[UniqueElement],
    result_list: list[int],
    elem_d: int,
) -> Generator[tuple[int, ...], None, None]

Provide helper function for unique_perms.

Parameters:

  • list_unique (list[UniqueElement]) –

    list[UniqueElement]

  • result_list (list[int]) –

    list[int]

  • elem_d (int) –

    int

Source code in toqito/perms/unique_perms.py 
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
def perm_unique_helper(
    list_unique: list[UniqueElement], result_list: list[int], elem_d: int,
) -> Generator[tuple[int, ...], None, None]:
    """Provide helper function for unique_perms.

    Args:
        list_unique: list[UniqueElement]
        result_list: list[int]
        elem_d: int

    """
    if elem_d < 0:
        yield tuple(result_list)
    else:
        for i in list_unique:
            if i.occurrences > 0:
                result_list[elem_d] = i.value
                i.occurrences -= 1
                yield from perm_unique_helper(list_unique, result_list, elem_d - 1)
                i.occurrences += 1